Question : Pipes A and B can fill a tank in 12 minutes and 15 minutes, respectively. The tank when full can be emptied by pipe C in $x$ minutes. When all three pipes are opened simultaneously, the tank is full in 10 minutes. The value of $x$ is:
Option 1: 18
Option 2: 15
Option 3: 20
Option 4: 24
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Correct Answer: 20
Solution : Pipe A can do 1 unit work = $\frac{1}{12}$ minutes Pipe B can do 1 unit work = $\frac{1}{15}$ minutes Pipe C can do 1 unit work = $-\frac{1}{x}$ minutes Together they can fill the tank = $\frac{1}{10}$ minutes Total work = Efficiency × days $⇒\frac{1}{\text{total days}} = \frac{1}{\text{A}} + \frac{1}{\text{B}} - \frac{1}{\text{C}}$ $⇒\frac{1}{10} = \frac{1}{12} + \frac{1}{15} - \frac{1}{x}$ $⇒\frac{1}{x} = \frac{1}{12} + \frac{1}{15} - \frac{1}{10}$ $⇒\frac{1}{x} = \frac{(5 + 4 - 6)}{60}$ $⇒\frac{1}{x} = \frac{3}{60}$ $\therefore x = 20$ Hence, the correct answer is 20.
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Question : Two pipes A and B can fill a tank in 12 minutes and 24 minutes, respectively, while a third pipe C can empty the full tank in 32 minutes. All three pipes are opened simultaneously. However, pipe C is closed 2 minutes before the tank is filled. In how much time (in minutes) will the tank be full?
Option 1: 9
Option 2: 10
Option 3: 12
Option 4: 8
Question : Pipes A, B and C can fill a tank in 20, 30 and 60 hours, respectively. Pipes A, B and C are opened at 7 a.m., 8 a.m., and 9 a.m., respectively, on the same day. When will the tank be full?
Option 1: 4:40 p.m.
Option 2: 5:40 p.m.
Option 3: 6:20 p.m.
Option 4: 7:20 p.m.
Question : Pipe A can fill 50% of the tank in 6 hours and Pipe B can fill the same tank in 18 hours. If both the pipes are opened simultaneously, how much time (in minutes) will the empty tank be filled?
Option 1: 420
Option 2: 425
Option 3: 432
Option 4: 435
Question : An inlet pipe can fill an empty tank in 140 hours, while an outlet pipe drains a filled tank in 63 hours. If 8 inlet pipes and y outlet pipes are opened simultaneously, when the tank is empty, then the tank gets filled in 105 hours. Find the value of y.
Option 1: 1
Option 2: 4
Option 3: 2
Option 4: 3
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